﻿namespace ProblemsSet
{
    public class Problem_72 : BaseProblem
    {
        public override object GetResult()
        {
            const int max = 1000000;

            long res = 0;
            for (long d = 2; d <= max; d++)
            {
                res += MathLogic.Phi(d);
            }
            return res;
        }

        public override string Problem
        {
            get
            {
                return @"Consider the fraction, n/d, where n and d are positive integers. If nd and HCF(n,d)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for d  8 in ascending order of size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that there are 21 elements in this set.

How many elements would be contained in the set of reduced proper fractions for d 1,000,000?";
            }
        }

        public override bool IsSolved
        {
            get
            {
                return true;
            }
        }

        public override object Answer
        {
            get
            {
                return 303963552391;
            }
        }

    }
}
